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Area of Science:

  • Network science
  • Complex systems analysis
  • Graph theory

Background:

  • K-core decomposition identifies network structures crucial for system dynamics like contagion and consensus.
  • Empirical network k-core structures often defy explanations based solely on node degree or standard random graph models.

Purpose of the Study:

  • To investigate the role of community structure in explaining the k-core decomposition of empirical networks.
  • To compare the k-core decomposition of real-world networks with randomized versions that preserve community information.

Main Methods:

  • Analysis of k-core decomposition in empirical networks.
  • Generation and analysis of randomized network models that incorporate community structure.
  • Comparison of k-core shell distributions between empirical and randomized networks.

Main Results:

  • Preserving community structure during network randomization is essential for replicating empirical k-core decomposition.
  • Node distribution within innermost k-shells is often concentrated in specific communities in certain networks.

Conclusions:

  • Community structure significantly influences the k-core organization of networks.
  • Random graph models must account for community structure to accurately represent empirical network properties related to k-cores.